Turkish investigators have released some information, saying the writer was tricked into going to the Saudi consulate in Istanbul on Oct. 2, where a 15-man hit team was waiting for him. They tortured him by cutting off his fingers and then dismembered and decapitated him, they said.
In the next few days, Erdogan said he will explain how the Saudis covered up the killing.
"We will reveal it," Erdogan said. "It will be revealed in full nakedness. Why did these 15 people come here? Why were 18 people arrested? All of this need to be explained."
Turkish intelligence has used passport scans that show the identities of some of the suspected hit men, saying they include some in the Saudi royal family's inner circle.
Saudi officials say Khashoggi, a U.S. resident and Washington Post columnist, was strangled after a fight with intelligence agents who wanted him to return to Saudi Arabia. The royal family said it didn't know what had happened for more than two weeks.
By challenging Riyadh's version of the story, Turkey could send shock waves throughout the Middle East, especially if bin Salman is implicated. Saudi Arabia plays a critical role in the alliance to fight Islamic extremists.
Surveillance video shows Khashoggi walk into the consulate on Oct. 2, leaving his fiancee outside. The Turkish government released new footage that shows a man identified as Mustafa al-Madani, walk out a few hours later wearing Khashoggi's clothes, a fake beard and glasses. The only difference is the al-Madani's shoes don't match.
The man, apparently a body double, was captured on camera at multiple locations around Istanbul, eventually going into a bathroom to change into his own clothes. He's then seen throwing a bag into the trash.
The backlash from the diplomatic crisis could be "the biggest event in the region since the Arab Spring," said Michael Stephens, a researcher at the Royal United Services Institute in London.
"Obviously, there's been deception and there's been lies," Trump told the Post. "Their stories are all over the place."
He said he didn't believe bin Salman should step down, calling him a "strong person.
"He has very good control. He's seen as a person who can keep things under check. I mean that in a positive way," he added.
Trump also said there's no evidence bin Salman knew about the plot to kill Khashoggi.
"There is a possibility he found out about it afterward," Trump said. "It could be something in the building went badly awry. It could be that's when he found out about it. He could have known they were bringing him back to Saudi Arabia."
The president has said previously those responsible would be severely punished.
A group of lawmakers has written a letter expressing outrage at the killing.
Britain, Germany and France issued a joint statement condemning the killing and calling for an "urgent need for clarification of exactly what happened."